11 Normal distribution problems - Empirical rule (from ck12.org)

%%html
<iframe width="700" height="400" src="https://www.youtube.com/embed/OhRr26AfFBU/" frameborder="0" allowfullscreen></iframe>

import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats

khanacademy

68–95–99.7 rule

credit: dataquest

mu = 9.5
sigma = 1.1

def cal_emperical_rule(mu, sigma):
    mu = 7 * [mu]
    sigma_scaler = np.arange(-3, 4, 1) 
    sigma_scales = sigma_scaler * sigma
    emperical_rule_lst = mu + sigma_scales
    return emperical_rule_lst

x = cal_emperical_rule(mu, sigma)

x

array([ 6.2,  7.3,  8.4,  9.5, 10.6, 11.7, 12.8])

sns.distplot(x)

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

<AxesSubplot:ylabel='Density'>